// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_CXX11_TENSOR_TENSOR_PADDING_H
#define EIGEN_CXX11_TENSOR_TENSOR_PADDING_H

namespace Eigen {

/** \class TensorPadding
 * \ingroup CXX11_Tensor_Module
 *
 * \brief Tensor padding class.
 * At the moment only padding with a constant value is supported.
 *
 */
namespace internal {
template<typename PaddingDimensions, typename XprType>
struct traits<TensorPaddingOp<PaddingDimensions, XprType>> : public traits<XprType>
{
	typedef typename XprType::Scalar Scalar;
	typedef traits<XprType> XprTraits;
	typedef typename XprTraits::StorageKind StorageKind;
	typedef typename XprTraits::Index Index;
	typedef typename XprType::Nested Nested;
	typedef typename remove_reference<Nested>::type _Nested;
	static const int NumDimensions = XprTraits::NumDimensions;
	static const int Layout = XprTraits::Layout;
	typedef typename XprTraits::PointerType PointerType;
};

template<typename PaddingDimensions, typename XprType>
struct eval<TensorPaddingOp<PaddingDimensions, XprType>, Eigen::Dense>
{
	typedef const TensorPaddingOp<PaddingDimensions, XprType>& type;
};

template<typename PaddingDimensions, typename XprType>
struct nested<TensorPaddingOp<PaddingDimensions, XprType>,
			  1,
			  typename eval<TensorPaddingOp<PaddingDimensions, XprType>>::type>
{
	typedef TensorPaddingOp<PaddingDimensions, XprType> type;
};

} // end namespace internal

template<typename PaddingDimensions, typename XprType>
class TensorPaddingOp : public TensorBase<TensorPaddingOp<PaddingDimensions, XprType>, ReadOnlyAccessors>
{
  public:
	typedef typename Eigen::internal::traits<TensorPaddingOp>::Scalar Scalar;
	typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
	typedef typename XprType::CoeffReturnType CoeffReturnType;
	typedef typename Eigen::internal::nested<TensorPaddingOp>::type Nested;
	typedef typename Eigen::internal::traits<TensorPaddingOp>::StorageKind StorageKind;
	typedef typename Eigen::internal::traits<TensorPaddingOp>::Index Index;

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorPaddingOp(const XprType& expr,
														  const PaddingDimensions& padding_dims,
														  const Scalar padding_value)
		: m_xpr(expr)
		, m_padding_dims(padding_dims)
		, m_padding_value(padding_value)
	{
	}

	EIGEN_DEVICE_FUNC
	const PaddingDimensions& padding() const { return m_padding_dims; }
	EIGEN_DEVICE_FUNC
	Scalar padding_value() const { return m_padding_value; }

	EIGEN_DEVICE_FUNC
	const typename internal::remove_all<typename XprType::Nested>::type& expression() const { return m_xpr; }

  protected:
	typename XprType::Nested m_xpr;
	const PaddingDimensions m_padding_dims;
	const Scalar m_padding_value;
};

// Eval as rvalue
template<typename PaddingDimensions, typename ArgType, typename Device>
struct TensorEvaluator<const TensorPaddingOp<PaddingDimensions, ArgType>, Device>
{
	typedef TensorPaddingOp<PaddingDimensions, ArgType> XprType;
	typedef typename XprType::Index Index;
	static const int NumDims = internal::array_size<PaddingDimensions>::value;
	typedef DSizes<Index, NumDims> Dimensions;
	typedef typename XprType::Scalar Scalar;
	typedef typename XprType::CoeffReturnType CoeffReturnType;
	typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
	static const int PacketSize = PacketType<CoeffReturnType, Device>::size;
	typedef StorageMemory<CoeffReturnType, Device> Storage;
	typedef typename Storage::Type EvaluatorPointerType;

	enum
	{
		IsAligned = true,
		PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
		BlockAccess = TensorEvaluator<ArgType, Device>::RawAccess,
		PreferBlockAccess = true,
		Layout = TensorEvaluator<ArgType, Device>::Layout,
		CoordAccess = true,
		RawAccess = false
	};

	typedef typename internal::remove_const<Scalar>::type ScalarNoConst;

	//===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
	typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
	typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;

	typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumDims, Layout, Index> TensorBlock;
	//===--------------------------------------------------------------------===//

	EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
		: m_impl(op.expression(), device)
		, m_padding(op.padding())
		, m_paddingValue(op.padding_value())
		, m_device(device)
	{
		// The padding op doesn't change the rank of the tensor. Directly padding a scalar would lead
		// to a vector, which doesn't make sense. Instead one should reshape the scalar into a vector
		// of 1 element first and then pad.
		EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);

		// Compute dimensions
		m_dimensions = m_impl.dimensions();
		for (int i = 0; i < NumDims; ++i) {
			m_dimensions[i] += m_padding[i].first + m_padding[i].second;
		}
		const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
		if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
			m_inputStrides[0] = 1;
			m_outputStrides[0] = 1;
			for (int i = 1; i < NumDims; ++i) {
				m_inputStrides[i] = m_inputStrides[i - 1] * input_dims[i - 1];
				m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1];
			}
			m_outputStrides[NumDims] = m_outputStrides[NumDims - 1] * m_dimensions[NumDims - 1];
		} else {
			m_inputStrides[NumDims - 1] = 1;
			m_outputStrides[NumDims] = 1;
			for (int i = NumDims - 2; i >= 0; --i) {
				m_inputStrides[i] = m_inputStrides[i + 1] * input_dims[i + 1];
				m_outputStrides[i + 1] = m_outputStrides[i + 2] * m_dimensions[i + 1];
			}
			m_outputStrides[0] = m_outputStrides[1] * m_dimensions[0];
		}
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }

	EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType)
	{
		m_impl.evalSubExprsIfNeeded(NULL);
		return true;
	}

#ifdef EIGEN_USE_THREADS
	template<typename EvalSubExprsCallback>
	EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(EvaluatorPointerType, EvalSubExprsCallback done)
	{
		m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
	}
#endif // EIGEN_USE_THREADS

	EIGEN_STRONG_INLINE void cleanup() { m_impl.cleanup(); }

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
	{
		eigen_assert(index < dimensions().TotalSize());
		Index inputIndex = 0;
		if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
			EIGEN_UNROLL_LOOP
			for (int i = NumDims - 1; i > 0; --i) {
				const Index idx = index / m_outputStrides[i];
				if (isPaddingAtIndexForDim(idx, i)) {
					return m_paddingValue;
				}
				inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
				index -= idx * m_outputStrides[i];
			}
			if (isPaddingAtIndexForDim(index, 0)) {
				return m_paddingValue;
			}
			inputIndex += (index - m_padding[0].first);
		} else {
			EIGEN_UNROLL_LOOP
			for (int i = 0; i < NumDims - 1; ++i) {
				const Index idx = index / m_outputStrides[i + 1];
				if (isPaddingAtIndexForDim(idx, i)) {
					return m_paddingValue;
				}
				inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
				index -= idx * m_outputStrides[i + 1];
			}
			if (isPaddingAtIndexForDim(index, NumDims - 1)) {
				return m_paddingValue;
			}
			inputIndex += (index - m_padding[NumDims - 1].first);
		}
		return m_impl.coeff(inputIndex);
	}

	template<int LoadMode>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
	{
		if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
			return packetColMajor(index);
		}
		return packetRowMajor(index);
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const
	{
		TensorOpCost cost = m_impl.costPerCoeff(vectorized);
		if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
			EIGEN_UNROLL_LOOP
			for (int i = 0; i < NumDims; ++i)
				updateCostPerDimension(cost, i, i == 0);
		} else {
			EIGEN_UNROLL_LOOP
			for (int i = NumDims - 1; i >= 0; --i)
				updateCostPerDimension(cost, i, i == NumDims - 1);
		}
		return cost;
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::TensorBlockResourceRequirements getResourceRequirements() const
	{
		const size_t target_size = m_device.lastLevelCacheSize();
		return internal::TensorBlockResourceRequirements::merge(
			internal::TensorBlockResourceRequirements::skewed<Scalar>(target_size), m_impl.getResourceRequirements());
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock block(TensorBlockDesc& desc,
															TensorBlockScratch& scratch,
															bool /*root_of_expr_ast*/ = false) const
	{
		// If one of the dimensions is zero, return empty block view.
		if (desc.size() == 0) {
			return TensorBlock(internal::TensorBlockKind::kView, NULL, desc.dimensions());
		}

		static const bool IsColMajor = Layout == static_cast<int>(ColMajor);
		const int inner_dim_idx = IsColMajor ? 0 : NumDims - 1;

		Index offset = desc.offset();

		// Compute offsets in the output tensor corresponding to the desc.offset().
		DSizes<Index, NumDims> output_offsets;
		for (int i = NumDims - 1; i > 0; --i) {
			const int dim = IsColMajor ? i : NumDims - i - 1;
			const int stride_dim = IsColMajor ? dim : dim + 1;
			output_offsets[dim] = offset / m_outputStrides[stride_dim];
			offset -= output_offsets[dim] * m_outputStrides[stride_dim];
		}
		output_offsets[inner_dim_idx] = offset;

		// Offsets in the input corresponding to output offsets.
		DSizes<Index, NumDims> input_offsets = output_offsets;
		for (int i = 0; i < NumDims; ++i) {
			const int dim = IsColMajor ? i : NumDims - i - 1;
			input_offsets[dim] = input_offsets[dim] - m_padding[dim].first;
		}

		// Compute offset in the input buffer (at this point it might be illegal and
		// point outside of the input buffer, because we don't check for negative
		// offsets, it will be autocorrected in the block iteration loop below).
		Index input_offset = 0;
		for (int i = 0; i < NumDims; ++i) {
			const int dim = IsColMajor ? i : NumDims - i - 1;
			input_offset += input_offsets[dim] * m_inputStrides[dim];
		}

		// Destination buffer and scratch buffer both indexed from 0 and have the
		// same dimensions as the requested block (for destination buffer this
		// property is guaranteed by `desc.destination()`).
		Index output_offset = 0;
		const DSizes<Index, NumDims> output_strides = internal::strides<Layout>(desc.dimensions());

		// NOTE(ezhulenev): We initialize bock iteration state for `NumDims - 1`
		// dimensions, skipping innermost dimension. In theory it should be possible
		// to squeeze matching innermost dimensions, however in practice that did
		// not show any improvements in benchmarks. Also in practice first outer
		// dimension usually has padding, and will prevent squeezing.

		// Initialize output block iterator state. Dimension in this array are
		// always in inner_most -> outer_most order (col major layout).
		array<BlockIteratorState, NumDims - 1> it;
		for (int i = 0; i < NumDims - 1; ++i) {
			const int dim = IsColMajor ? i + 1 : NumDims - i - 2;
			it[i].count = 0;
			it[i].size = desc.dimension(dim);

			it[i].input_stride = m_inputStrides[dim];
			it[i].input_span = it[i].input_stride * (it[i].size - 1);

			it[i].output_stride = output_strides[dim];
			it[i].output_span = it[i].output_stride * (it[i].size - 1);
		}

		const Index input_inner_dim_size = static_cast<Index>(m_impl.dimensions()[inner_dim_idx]);

		// Total output size.
		const Index output_size = desc.size();

		// We will fill inner dimension of this size in the output. It might be
		// larger than the inner dimension in the input, so we might have to pad
		// before/after we copy values from the input inner dimension.
		const Index output_inner_dim_size = desc.dimension(inner_dim_idx);

		// How many values to fill with padding BEFORE reading from the input inner
		// dimension.
		const Index output_inner_pad_before_size =
			input_offsets[inner_dim_idx] < 0
				? numext::mini(numext::abs(input_offsets[inner_dim_idx]), output_inner_dim_size)
				: 0;

		// How many values we can actually copy from the input inner dimension.
		const Index output_inner_copy_size = numext::mini(
			// Want to copy from input.
			(output_inner_dim_size - output_inner_pad_before_size),
			// Can copy from input.
			numext::maxi(input_inner_dim_size - (input_offsets[inner_dim_idx] + output_inner_pad_before_size),
						 Index(0)));

		eigen_assert(output_inner_copy_size >= 0);

		// How many values to fill with padding AFTER reading from the input inner
		// dimension.
		const Index output_inner_pad_after_size =
			(output_inner_dim_size - output_inner_copy_size - output_inner_pad_before_size);

		// Sanity check, sum of all sizes must be equal to the output size.
		eigen_assert(output_inner_dim_size ==
					 (output_inner_pad_before_size + output_inner_copy_size + output_inner_pad_after_size));

		// Keep track of current coordinates and padding in the output.
		DSizes<Index, NumDims> output_coord = output_offsets;
		DSizes<Index, NumDims> output_padded;
		for (int i = 0; i < NumDims; ++i) {
			const int dim = IsColMajor ? i : NumDims - i - 1;
			output_padded[dim] = isPaddingAtIndexForDim(output_coord[dim], dim);
		}

		typedef internal::StridedLinearBufferCopy<ScalarNoConst, Index> LinCopy;

		// Prepare storage for the materialized padding result.
		const typename TensorBlock::Storage block_storage = TensorBlock::prepareStorage(desc, scratch);

		// TODO(ezhulenev): Squeeze multiple non-padded inner dimensions into a
		// single logical inner dimension.

		// When possible we squeeze writes for the innermost (only if non-padded)
		// dimension with the first padded dimension. This allows to reduce the
		// number of calls to LinCopy and better utilize vector instructions.
		const bool squeeze_writes = NumDims > 1 &&
									// inner dimension is not padded
									(input_inner_dim_size == m_dimensions[inner_dim_idx]) &&
									// and equal to the block inner dimension
									(input_inner_dim_size == output_inner_dim_size);

		const int squeeze_dim = IsColMajor ? inner_dim_idx + 1 : inner_dim_idx - 1;

		// Maximum coordinate on a squeeze dimension that we can write to.
		const Index squeeze_max_coord =
			squeeze_writes ? numext::mini(
								 // max non-padded element in the input
								 static_cast<Index>(m_dimensions[squeeze_dim] - m_padding[squeeze_dim].second),
								 // max element in the output buffer
								 static_cast<Index>(output_offsets[squeeze_dim] + desc.dimension(squeeze_dim)))
						   : static_cast<Index>(0);

		// Iterate copying data from `m_impl.data()` to the output buffer.
		for (Index size = 0; size < output_size;) {
			// Detect if we are in the padded region (exclude innermost dimension).
			bool is_padded = false;
			for (int j = 1; j < NumDims; ++j) {
				const int dim = IsColMajor ? j : NumDims - j - 1;
				is_padded = output_padded[dim];
				if (is_padded)
					break;
			}

			if (is_padded) {
				// Fill single innermost dimension with padding value.
				size += output_inner_dim_size;

				LinCopy::template Run<LinCopy::Kind::FillLinear>(
					typename LinCopy::Dst(output_offset, 1, block_storage.data()),
					typename LinCopy::Src(0, 0, &m_paddingValue),
					output_inner_dim_size);

			} else if (squeeze_writes) {
				// Squeeze multiple reads from innermost dimensions.
				const Index squeeze_num = squeeze_max_coord - output_coord[squeeze_dim];
				size += output_inner_dim_size * squeeze_num;

				// Copy `squeeze_num` inner dimensions from input to output.
				LinCopy::template Run<LinCopy::Kind::Linear>(
					typename LinCopy::Dst(output_offset, 1, block_storage.data()),
					typename LinCopy::Src(input_offset, 1, m_impl.data()),
					output_inner_dim_size * squeeze_num);

				// Update iteration state for only `squeeze_num - 1` processed inner
				// dimensions, because we have another iteration state update at the end
				// of the loop that will update iteration state for the last inner
				// processed dimension.
				it[0].count += (squeeze_num - 1);
				input_offset += it[0].input_stride * (squeeze_num - 1);
				output_offset += it[0].output_stride * (squeeze_num - 1);
				output_coord[squeeze_dim] += (squeeze_num - 1);

			} else {
				// Single read from innermost dimension.
				size += output_inner_dim_size;

				{ // Fill with padding before copying from input inner dimension.
					const Index out = output_offset;

					LinCopy::template Run<LinCopy::Kind::FillLinear>(
						typename LinCopy::Dst(out, 1, block_storage.data()),
						typename LinCopy::Src(0, 0, &m_paddingValue),
						output_inner_pad_before_size);
				}

				{ // Copy data from input inner dimension.
					const Index out = output_offset + output_inner_pad_before_size;
					const Index in = input_offset + output_inner_pad_before_size;

					eigen_assert(output_inner_copy_size == 0 || m_impl.data() != NULL);

					LinCopy::template Run<LinCopy::Kind::Linear>(typename LinCopy::Dst(out, 1, block_storage.data()),
																 typename LinCopy::Src(in, 1, m_impl.data()),
																 output_inner_copy_size);
				}

				{ // Fill with padding after copying from input inner dimension.
					const Index out = output_offset + output_inner_pad_before_size + output_inner_copy_size;

					LinCopy::template Run<LinCopy::Kind::FillLinear>(
						typename LinCopy::Dst(out, 1, block_storage.data()),
						typename LinCopy::Src(0, 0, &m_paddingValue),
						output_inner_pad_after_size);
				}
			}

			for (int j = 0; j < NumDims - 1; ++j) {
				const int dim = IsColMajor ? j + 1 : NumDims - j - 2;

				if (++it[j].count < it[j].size) {
					input_offset += it[j].input_stride;
					output_offset += it[j].output_stride;
					output_coord[dim] += 1;
					output_padded[dim] = isPaddingAtIndexForDim(output_coord[dim], dim);
					break;
				}
				it[j].count = 0;
				input_offset -= it[j].input_span;
				output_offset -= it[j].output_span;
				output_coord[dim] -= it[j].size - 1;
				output_padded[dim] = isPaddingAtIndexForDim(output_coord[dim], dim);
			}
		}

		return block_storage.AsTensorMaterializedBlock();
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvaluatorPointerType data() const { return NULL; }

#ifdef EIGEN_USE_SYCL
	// binding placeholder accessors to a command group handler for SYCL
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler& cgh) const { m_impl.bind(cgh); }
#endif

  private:
	struct BlockIteratorState
	{
		BlockIteratorState()
			: count(0)
			, size(0)
			, input_stride(0)
			, input_span(0)
			, output_stride(0)
			, output_span(0)
		{
		}

		Index count;
		Index size;
		Index input_stride;
		Index input_span;
		Index output_stride;
		Index output_span;
	};

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isPaddingAtIndexForDim(Index index, int dim_index) const
	{
#if defined(EIGEN_HAS_INDEX_LIST)
		return (!internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0) &&
				index < m_padding[dim_index].first) ||
			   (!internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0) &&
				index >= m_dimensions[dim_index] - m_padding[dim_index].second);
#else
		return (index < m_padding[dim_index].first) || (index >= m_dimensions[dim_index] - m_padding[dim_index].second);
#endif
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isLeftPaddingCompileTimeZero(int dim_index) const
	{
#if defined(EIGEN_HAS_INDEX_LIST)
		return internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0);
#else
		EIGEN_UNUSED_VARIABLE(dim_index);
		return false;
#endif
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isRightPaddingCompileTimeZero(int dim_index) const
	{
#if defined(EIGEN_HAS_INDEX_LIST)
		return internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0);
#else
		EIGEN_UNUSED_VARIABLE(dim_index);
		return false;
#endif
	}

	void updateCostPerDimension(TensorOpCost& cost, int i, bool first) const
	{
		const double in = static_cast<double>(m_impl.dimensions()[i]);
		const double out = in + m_padding[i].first + m_padding[i].second;
		if (out == 0)
			return;
		const double reduction = in / out;
		cost *= reduction;
		if (first) {
			cost += TensorOpCost(
				0, 0, 2 * TensorOpCost::AddCost<Index>() + reduction * (1 * TensorOpCost::AddCost<Index>()));
		} else {
			cost +=
				TensorOpCost(0,
							 0,
							 2 * TensorOpCost::AddCost<Index>() + 2 * TensorOpCost::MulCost<Index>() +
								 reduction * (2 * TensorOpCost::MulCost<Index>() + 1 * TensorOpCost::DivCost<Index>()));
		}
	}

  protected:
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetColMajor(Index index) const
	{
		EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
		eigen_assert(index + PacketSize - 1 < dimensions().TotalSize());

		const Index initialIndex = index;
		Index inputIndex = 0;
		EIGEN_UNROLL_LOOP
		for (int i = NumDims - 1; i > 0; --i) {
			const Index firstIdx = index;
			const Index lastIdx = index + PacketSize - 1;
			const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i];
			const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i];
			const Index lastPaddedRight = m_outputStrides[i + 1];

			if (!isLeftPaddingCompileTimeZero(i) && lastIdx < lastPaddedLeft) {
				// all the coefficient are in the padding zone.
				return internal::pset1<PacketReturnType>(m_paddingValue);
			} else if (!isRightPaddingCompileTimeZero(i) && firstIdx >= firstPaddedRight && lastIdx < lastPaddedRight) {
				// all the coefficient are in the padding zone.
				return internal::pset1<PacketReturnType>(m_paddingValue);
			} else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) ||
					   (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
				// all the coefficient are between the 2 padding zones.
				const Index idx = index / m_outputStrides[i];
				inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
				index -= idx * m_outputStrides[i];
			} else {
				// Every other case
				return packetWithPossibleZero(initialIndex);
			}
		}

		const Index lastIdx = index + PacketSize - 1;
		const Index firstIdx = index;
		const Index lastPaddedLeft = m_padding[0].first;
		const Index firstPaddedRight = (m_dimensions[0] - m_padding[0].second);
		const Index lastPaddedRight = m_outputStrides[1];

		if (!isLeftPaddingCompileTimeZero(0) && lastIdx < lastPaddedLeft) {
			// all the coefficient are in the padding zone.
			return internal::pset1<PacketReturnType>(m_paddingValue);
		} else if (!isRightPaddingCompileTimeZero(0) && firstIdx >= firstPaddedRight && lastIdx < lastPaddedRight) {
			// all the coefficient are in the padding zone.
			return internal::pset1<PacketReturnType>(m_paddingValue);
		} else if ((isLeftPaddingCompileTimeZero(0) && isRightPaddingCompileTimeZero(0)) ||
				   (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
			// all the coefficient are between the 2 padding zones.
			inputIndex += (index - m_padding[0].first);
			return m_impl.template packet<Unaligned>(inputIndex);
		}
		// Every other case
		return packetWithPossibleZero(initialIndex);
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetRowMajor(Index index) const
	{
		EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
		eigen_assert(index + PacketSize - 1 < dimensions().TotalSize());

		const Index initialIndex = index;
		Index inputIndex = 0;
		EIGEN_UNROLL_LOOP
		for (int i = 0; i < NumDims - 1; ++i) {
			const Index firstIdx = index;
			const Index lastIdx = index + PacketSize - 1;
			const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i + 1];
			const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i + 1];
			const Index lastPaddedRight = m_outputStrides[i];

			if (!isLeftPaddingCompileTimeZero(i) && lastIdx < lastPaddedLeft) {
				// all the coefficient are in the padding zone.
				return internal::pset1<PacketReturnType>(m_paddingValue);
			} else if (!isRightPaddingCompileTimeZero(i) && firstIdx >= firstPaddedRight && lastIdx < lastPaddedRight) {
				// all the coefficient are in the padding zone.
				return internal::pset1<PacketReturnType>(m_paddingValue);
			} else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) ||
					   (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
				// all the coefficient are between the 2 padding zones.
				const Index idx = index / m_outputStrides[i + 1];
				inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
				index -= idx * m_outputStrides[i + 1];
			} else {
				// Every other case
				return packetWithPossibleZero(initialIndex);
			}
		}

		const Index lastIdx = index + PacketSize - 1;
		const Index firstIdx = index;
		const Index lastPaddedLeft = m_padding[NumDims - 1].first;
		const Index firstPaddedRight = (m_dimensions[NumDims - 1] - m_padding[NumDims - 1].second);
		const Index lastPaddedRight = m_outputStrides[NumDims - 1];

		if (!isLeftPaddingCompileTimeZero(NumDims - 1) && lastIdx < lastPaddedLeft) {
			// all the coefficient are in the padding zone.
			return internal::pset1<PacketReturnType>(m_paddingValue);
		} else if (!isRightPaddingCompileTimeZero(NumDims - 1) && firstIdx >= firstPaddedRight &&
				   lastIdx < lastPaddedRight) {
			// all the coefficient are in the padding zone.
			return internal::pset1<PacketReturnType>(m_paddingValue);
		} else if ((isLeftPaddingCompileTimeZero(NumDims - 1) && isRightPaddingCompileTimeZero(NumDims - 1)) ||
				   (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
			// all the coefficient are between the 2 padding zones.
			inputIndex += (index - m_padding[NumDims - 1].first);
			return m_impl.template packet<Unaligned>(inputIndex);
		}
		// Every other case
		return packetWithPossibleZero(initialIndex);
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const
	{
		EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];
		EIGEN_UNROLL_LOOP
		for (int i = 0; i < PacketSize; ++i) {
			values[i] = coeff(index + i);
		}
		PacketReturnType rslt = internal::pload<PacketReturnType>(values);
		return rslt;
	}

	Dimensions m_dimensions;
	array<Index, NumDims + 1> m_outputStrides;
	array<Index, NumDims> m_inputStrides;
	TensorEvaluator<ArgType, Device> m_impl;
	PaddingDimensions m_padding;

	Scalar m_paddingValue;

	const Device EIGEN_DEVICE_REF m_device;
};

} // end namespace Eigen

#endif // EIGEN_CXX11_TENSOR_TENSOR_PADDING_H
